Question

Segment AB is congruent to segment BE, segment BF is congruent to segment BC. Prove: Segment BG is congruent to segment BD.

a) Geometry
b) Algebra
c) History
d) Other

Answer 1

To prove that segment BG is congruent to segment BD, we can use the ASA (angle-side-angle) congruence theorem. By showing that triangles ABE and BCF are congruent, we can conclude that segment BG is congruent to segment BD.

Step-by-step explanation:

In order to prove that segment BG is congruent to segment BD, we can use the ASA (angle-side-angle) congruence theorem. Here are the steps:

First, since segment AB is congruent to segment BE and segment BF is congruent to segment BC, we can say that triangles ABE and BCF are congruent by the SSS (side-side-side) congruence theorem.

Next, since triangles ABE and BCF are congruent, we can conclude that angle AEB is congruent to angle BFC and angle BAE is congruent to angle BCF by the corresponding parts of congruent triangles.

Finally, since angle BAE is congruent to angle BCF, and segment AB is congruent to segment BE, we can use the ASA congruence theorem to conclude that segment BG is congruent to segment BD.